Controlling selection rules for magnon scattering in nanomagnets by spatial symmetry breaking

Nanomagnets are the building blocks of many existing and emergent spintronic technologies. Magnetization dynamics of nanomagnets is often dominated by nonlinear processes, which have been recently shown to have many surprising features and far-reaching implications for applications. Here we develop a theoretical framework uncovering the selection rules for multimagnon processes and discuss their underlying mechanisms. For its technological relevance, we focus on the degenerate three-magnon process in thin elliptical nanodisks to illustrate our findings. We parameterize the selection rules through a set of magnon interaction coefficients which we calculate using micromagnetic simulations. We postulate the selection rules and investigate how they are altered by perturbations, that break the symmetry of static magnetization configuration and spatial spin-wave profiles and that can be realized by applying off-symmetry-axis or nonuniform magnetic fields. Our work provides the phenomenological understanding into the mechanics of magnon interaction as well as the formalism for determining the interaction coefficients from simulations and experimental data. Our results serve as a guide to analyze magnon processes inherently present in spin-torque devices for boosting their performance or to engineer a specific nonlinear response of a nanomagnet used in neuromorphic or quantum magnonic application.